excitation transfer in photosynthetic pigment protein...
TRANSCRIPT
Excitation Transfer in Photosynthetic Pigment Protein Complexes
Tomáš Mančal
Faculty of Mathematics and Physics Charles University, Prague
Ke Karlovu 5, 121 16 Prague 2, Czech Republic
Open questions on energy transport & conversionin nanoscale quantum systems
Marseille, November 16th 2018
Outline
• Photosynthetic light-harvesting: a brief introduction
• Does in make sense to distinguish between the quantum and the classical?: a brief history of a controversy
• What is quantum on photosynthetic energy transfer? (This question is related to thermodynamics behavior)
Quantum-coherent weakly driven thermal machines can be simulated classically
Talk right after me:Luis. A. CorreaQuantum-coherent weakly driven thermal machines can be simulated classically
Photosynthesis
Photosynthesis: Biology, Chemistry or Physics?
6 CO2 + 12 H2O → C6H12O6 + 6 O2 + 6 H2O
A school definition
A row of complicated physical, chemicaland biological processes
Interesting for physicists: primary processes in photosynthesisPhoton captureExcitation energy transfer towards reaction centerElectron transfer in reaction centerTransfer of protons across cellular membrane
Photosynthesis done not just by plants, but also by bacteria
Photosynthetic Antennae
Photosynthesis always occurs on membranes
Photosynthetic bacterium
Invaginations on the innercellular wall
Two separatedaquatic environments
reaction center
various light harvesting antennae
Photosynthetic Antennae
Scheuring et al. The EMBO J. 20 (2001) 3029
Sun light = a rather sparse source of energy
Antenna
Reactioncenter
Photosynthetic Antennae
• Highly organized structure
• Fixed spatial relations between individual pigments
• Very few types of buildingblocks
• Protein play major role in establishing structure andmodulating electronic properties
• Photon capture
• Energy transfer
• Electron transfer
• Proton transfer
• ATP production
• Other cellular processes including carbon fixation and oxygen production
Physics
Chemistry
Biology
Timescale difference!
Place of Photosynthesis in Natural Sciences
Quantum/Classical Controversy in Photosynthetic Research
Brief (Biased) History of the Controversy
2005 – Brixner et. al, Nature 434 (2005) 625optical/near IR analogues of coherent NMR experiments on Photosyntheticsystems - Coherent 2D Electronic Spectroscopy (2DES)
2006 – Pisliakov et. al, J. Chem. Phys. 124 (2006) 234505prediction of oscillations in 2DES due to electronic coherence; dephasing timespredicted for Fenna-Matthews-Olson (FMO) complex
2007 – Engel et. al, Nature 446 (2007) 782detection of the predicted oscillations - much longer than expected life-timesclaims: oscillations = electronic coherence; electronic coherence importantfor the efficiency of energy transfer in photosynthesis; perhaps photosyntheticsystems are actually quantum computers
2008 and onMany theoretical papers on quantumness of photosynthesisClaims: quantum entanglement is the cause of the efficiency;
entanglement survives unusually long etc.
Brief (Biased) History of the Controversy
Essential claim of the new theoretical papers:• Now we formulate quantum theory of energy transfer (before it was described classically)• Quantum means coherent, coherent means entanglement• Coherence enables efficient energy transfer in space• Coherent motion induced not only by laser light, but also by natural (sunlight) illumination
Some counter arguments• Coherent does not mean necessarily quantum
o There is a classical coherence: W. H. Miller, J. Chem. Phys. 136 (2012) 210901o Coherent states of light are actually as classical as it gets: Any quantum optics book
• Coherent dynamics of photosynthetic (Frenkel) excitons is classicalo They can be mapped on a system of harmonic oscillators
S. Mukamel, J. Chem. Phys. 132 (2010) 241105,J. S. Briggs and A. Eisfeld, Phys. Rev. E 83 (2011) 051911
o Only the thermodynamic downhill preference in energy transfer is a genuinely quantum effect: T. Mancal, J. Phys. Chem. B, 117 (2013) 11282
• Sunlight does not induce any time-dependent coherence (photon is not a bullet)o One must not mix statistical interpretation of quantum mechanics with what is “actually” going on: T. Mančal and L. Valkunas, New J. Phys. 12 (2010) 065044
Brief (Biased) History of the Controversy
Quantum theory of photosynthesis• It is so old that there are textbooks on it
van Amerongen, Valkunas, van Grondelle, Photosynthetic excitons, World Scientific, 2000
May & Kuehn, Charge and Energy Transfer Dynamics in Molecular Systems, Wiley-VCH, 2000
for comparison
• Plenio, Engel (eds.) Quantum Effects in Biological Systems, (2014) does literally not containa single equation not found in the two books above
S. Mukamel, J. Phys. Chem. A 117 (2013) 10563Comment on “Coherence and Uncertainty in Nanostructured Organic Photovoltaics”In summary, exciton coherence and localization are well established concepts dating backto the 1970s that are constantly being rediscovered and recast with a different terminology, earlier in biological light harvesting and now in photovoltaics. There is nothing particularly surprising in the recent biological or photovoltaic experiments that require paradigm change.
The Quantum and The Classical
- certainly not the theorists: only quantum mechanics is used, nothing else
Who cares if photosynthesis is quantum or classical?
- certainly not the experimentalists: they know it is quantum
+ future quantum technologists
The question of Quantum vs. Classical photosynthesis is not a purely academic one.It is very practical:
Should we expect some counter intuitive, hard to imagine and hard to understand behavior in photosynthetic antennae?
Quantum Photosynthesis
What is Quantum in Photosynthesis
Classical picture of photosynthetic antenna?
T. Mancal, J. Phys. Chem. B 117 (2013) 11282
-
Lorentz theory of absorption (1910)
+
Electrically neutral atom (molecule)
xy
zElectron is displaced by interaction with light
-+
displacementincoming field
polarization
wave vector
r
k
e
What is Quantum in Photosynthesis
Classical picture of photosynthetic antenna?
T. Mancal, J. Phys. Chem. B 117 (2013) 11282
Classical equations for electronic displacement
• Identification of electronic oscillator amplitude with electronic (optical) coherence• Perfect mapping of Schrödinger equation for excitons on a set of oscillators
Pointed out by MukamelStudied in detail by Briggs and Eisfeld
Equation of motion for a set of (classical) harmonic oscillators coupled to a reservoir
Amplitude of n-th oscillatorCoupling between oscillators
Modulation of frequency by bath
What is Quantum in Photosynthesis
Classical picture of photosynthetic antenna?
T. Mancal, J. Phys. Chem. B 117 (2013) 11282
slow
We can take this away
Canonical quasi-equilibrium establishes here
Classical equations do not show any preference for downhill transfer
(Correct) thermodynamic behavior is the only uniquely quantum featureof Frenkel exciton energy transfer
g
1e2e
3e
Entanglement and Thermodynamics
In J. Phys. Chem. B 117 (2013) 11282 – derivation by analogy
Here – derivation of classical oscillator equations from quantum mechanical equations for excitons in photosynthetic antenna
Schrödinger equation
Decomposition into pointer states
Crucial property of the bath states relative to pointer states
Bath states
Entanglement and Thermodynamics
This is where the „observer“ is
Classical bath that does not entangle with the quantum mechanical system
Interaction picture with respect to the bath
Bath induced fluctuations
Entanglement and Thermodynamics
Bath can now be eliminated
Modulation throughexpectation value
One strange term
Entanglement and Thermodynamics
Global phase and its elimination
Global phase does notplay any role in physics
Entanglement and Thermodynamics
System-bath interaction – operator on system Hilbert space only!
Entanglement and Thermodynamics
Frenkel exciton Hamiltonian
Harmonic bath
State decomposition into collective excited states
Entanglement and Thermodynamics
Equations identical to the classical equations for oscilátor amplitudes
Bath introduced real valued transition frequency fluctuations
In a true quantum case,there is an operator here!
In the absence of system-bath entanglement, quantum system of excitons behaves entirely classically
Conclusions
• Coherent component of photosynthetic energy transfer can be perfectly mapped onto a classical system of oscillators
• Thermodynamic behavior (trapping) is a uniquely quantum feature of photosynthetic antennae
• Trapping is enabled by system-bath entanglement
Acknowledgement
Funding from Czech Science Foundation (GACR)
Neuron fund – private fund for support of basic science
Postdoc and PhD positions open
gments
Research groupJoachim SeibtPavel Malý Sayeh RajabiVladislav Sláma
Thank you for your attention
Open Quantum Systems from Wavefunction Perspective
Open (Quantum) Systems
• Quantum theory is a universal theory• Only the whole Universe can be considered ”isolated”• Microscopic systems can be considered isolated for in a limited time interval after a state preparation• We need quasi-isolated systems to test quantum theory
All things that exist are open quantum systems
Classical world emerges from the quantum world in the process of decoherence
• Features natural to quantum world (such as entanglement) seemingly disappear• It is those very features that make the classical world emerge• On a fundamental level everything remains quantum
Density Matrix vs. Wavefunction
Bath
System
State vector(a.k.a. wavefunction)
Statistical operator(a.k.a. density matrix)
Description of the combined system
Expectation values of the system quantities
Reduced density matrix
Some basis on bath
No reduced wavefunction is possible!
Can We Live without Density Matrix?
YES and NO
In some fields of chemistry (and physics) they never use (reduced) density matrix (see e.g. text book derivationsof excited state life time)
Methodology is well developed
Working with reduced density matrix is very convenient.Expectation values, i.e. analoguess or sections of reduced DMhave to be calculated anyway
We would loose „master equations“
Advantages of Wavefunction Formalism
1. We never loose sight of the bath
Basis states of the system
Probability amplitudes for the system „Relative“ state of the bath
Existence of „relative“ states of the bath goes to the heart of quantum mechanics• System and bath entangle with each other!
Relative bath states ARE states• no problem (not even philosophical) in talking about them• On the contrary – „relative“ density matrices of the bath ARE NOT states
Beware of spectroscopic speak!!!
Advantages of Wavefunction Formalism
2. Decoherence and dephasing are not confounded in wavefunction formalism
Ensemble and quantum mechanical averaging are cleanly separated
Decoherence – results from quantum mechanical averaging
Dephasing – results from ensemble averaging
)
Advantages of Wavefunction Formalism
3. Clear and concise way of speaking about the state of the system
In interpretations of quantum mechanics, which tend to be based on “classical terms” (classical observations) only, you are not allowed to speakabout certain things:
Where was the particle between measurements?What is a momentum of a particle?
These are inherently „density matrix“ questions.They assume there IS a particle without the rest of the Universe.
Keep thinking about the (complete) state!